1+2+2+2+2+3+2+4+2+5+2+6+2+2008+2+2009 1+2+2+2+2+3+2+4+2+5+2+6+... 2009 Power of..+2 1+2+2+2+2+3+2+4+2+5+2+6+2+2008+2+2009 1+2+2+2 Square+2 third power+2 fourth power+2 fifth power+2 sixth power+... 2009 Power of..+2

1+2+2+2+2+3+2+4+2+5+2+6+2+2008+2+2009 1+2+2+2+2+3+2+4+2+5+2+6+... 2009 Power of..+2 1+2+2+2+2+3+2+4+2+5+2+6+2+2008+2+2009 1+2+2+2 Square+2 third power+2 fourth power+2 fifth power+2 sixth power+... 2009 Power of..+2

Let y=1+2+2^2+2^3+...+2^2009
2Y=2+2^2+2^3+...+2^2010
2Y-y=y=2^2010-1

Calculation (-2)2002 power +(-2)2003 power

(-2)^2002+(-2)^2003
=2^2002-2^2003
=2^2002-2*2^2002
=-2^2002